Consider the financial contract x$/$t $=\{$x$0,$ x$1\}/\{$t$0,$ t$1\}$ with x$0=102,$ x$1=107,$

t$0=0,$ t$1=5$ months. Under the exponential law, calculate: $($a$)$ the annual interest rate ia;

$($b$)$ the quarterly interest rate i$4.$

Suppose to redefine the contract as x$/$t $=\{$x$0,$ x$1,$ x$2,$ x$3\}/\{$t$0,$ t$1,$ t$2,$ t$3\}$ with x$0=102,$ x$1=$

$107,$ x$2=$ X$,$ x$3=80,$ t$0=0,$ t$1=5$ months, t$2=7$ months and t$3=9$ months. Calculate the

value of X such that the contract x$/$t is fair, under the exponential law, assuming as interest

rate the interest ia $=15\%.$